How Do Gradients, Rates, and the Term 'Per' Relate to Division and Ratios?

[Miraj Kayastha]

Why does "per" in 3 miles per hour mean division?
Why are gradients and rates a ratio?

 

[Hardik Batra]

Why does "per" in 3 miles per hour mean division?

The meaning of "per" is "for each" .

Now read 3 miles "for each" hour.
And you divide the 3 miles by one hour you will get the speed of an object.

 

[256bits]

Why does "per" in 3 miles per hour mean division?
Why are gradients and rates a ratio?

Are you not familiar with the basic equation
y = mx + b
where m is the slope, or rate ( and b is the intercept )

m is the ratio of the ordinate to the abscissa for any point on the line (x,y)

If you plot y-axis as the "miles" and x-axis as the time of hours , then the slope naturally follows as miles/hour, or in English terms miles per hour.

Same thing for gradient - for a surface that has a slope, its elevation will increase y-amount for every x-amount distance.

 

[CWatters]

Why are gradients and rates a ratio?

Two "similar triangles" have the same angles but can be different sizes.

In each case

Tan{Θ} = Length of opposite side/length of adjacent side

So if interested in the angle or gradiant it makes sense to compare the ratio of the sides rather than their absolute magnitude.